Quantum Annealing for Neural Network optimization problems: a new approach via Tensor Network simulations

Abstract

Quantum Annealing (QA) is one of the most promising frameworks for quantum optimization. Here, we focus on the problem of minimizing complex classical cost functions associated with prototypical discrete neural networks, specifically the paradigmatic Hopfield model and binary perceptron. We show that the adiabatic time evolution of QA can be efficiently represented as a suitable Tensor Network. This representation allows for simple classical simulations, well-beyond small sizes amenable to exact diagonalization techniques. We show that the optimized state, expressed as a Matrix Product State (MPS), can be recast into a Quantum Circuit, whose depth scales only linearly with the system size and quadratically with the MPS bond dimension. This may represent a valuable starting point allowing for further circuit optimization on near-term quantum devices.

References in corpus (40)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• The density-matrix renormalization group in the age of matrix product states
• Variational Quantum Algorithms
• Ising formulations of many NP problems
• Efficient classical simulation of slightly entangled quantum computations
• Quantum Annealing in the Transverse Ising Model
• A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
• A Quantum Approximate Optimization Algorithm
• Adiabatic Quantum Computing
• Time-dependent variational principle for quantum lattices
• Theory of Quantum Annealing of an Ising Spin Glass
• Quantum Approximate Optimization Algorithm: Performance, Mechanism, and Implementation on Near-Term Devices
• Quantum Annealing: A New Method for Minimizing Multidimensional Functions
• Defining and detecting quantum speedup
• Digitized adiabatic quantum computing with a superconducting circuit
• Optimal Quantum Circuits for General Two-Qubit Gates
• QAOA for Max-Cut requires hundreds of qubits for quantum speed-up
• Variational quantum algorithms for nonlinear problems
• Unsupervised Generative Modeling Using Matrix Product States
• Real- and imaginary-time evolution with compressed quantum circuits
• Tangent-space methods for uniform matrix product states
• Lecture Notes of Tensor Network Contractions
• The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems
• Sequential Generation of Matrix-Product States in Cavity QED
• Machine learning with neural networks
• Supervised Learning with Quantum-Inspired Tensor Networks
• The Variational Power of Quantum Circuit Tensor Networks
• Many-body transverse interactions in the quantum annealing of the p-spin ferromagnet
• On quantum mean-field models and their quantum annealing
• Efficiency of quantum versus classical annealing in non-convex learning problems
• Quantum annealing of the $p$-spin model under inhomogeneous transverse field driving
• Efficient decomposition of unitary matrices in quantum circuit compilers
• Completely Quantum Neural Networks
• Quantum Annealing: a journey through Digitalization, Control, and hybrid Quantum Variational schemes
• Entropy landscape of solutions in the binary perceptron problem
• Optimal working point in digitized quantum annealing
• Constrained optimization of sequentially generated entangled multiqubit states
• Dynamics of the order-parameter statistics in the long-range Ising model
• Success of digital adiabatic simulation with large Trotter step
• The Quantum Approximate Optimization Algorithm performance with low entanglement and high circuit depth

Cited by in corpus (7)

• Towards adiabatic quantum computing using compressed quantum circuits
• Self-Correcting Quantum Many-Body Control using Reinforcement Learning with Tensor Networks
• Anticoncentration and state design of random tensor networks
• Fermionic Magic Resources of Quantum Many-Body Systems
• Beyond Quantum Annealing: Optimal control solutions to MaxCut problems
• Quantum circuit compilation with quantum computers
• Variational matrix product states for combinatorial optimization